/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    Eclipse Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
$begin sparse_sub_hes.cpp$$
$spell
$$

$section Subset of a Sparse Hessian: Example and Test$$

$head Purpose$$
This example uses a
$cref/column subset/sparse_hessian/p/Column Subset/$$ of the sparsity pattern
to compute a subset of the Hessian.

$head See Also$$
$cref sub_sparse_hes.cpp$$

$code
$srcfile%example/sparse/sparse_sub_hes.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
bool sparse_sub_hes(void)
{	bool ok = true;
	using CppAD::AD;
	typedef CPPAD_TESTVECTOR(size_t)     SizeVector;
	typedef CPPAD_TESTVECTOR(double)     DoubleVector;
	typedef CppAD::sparse_rc<SizeVector> sparsity;
	//
	// domain space vector
	size_t n = 4;
	CPPAD_TESTVECTOR(AD<double>) ax(n);
	for(size_t j = 0; j < n; j++)
		ax[j] = double(j);

	// declare independent variables and start recording
	CppAD::Independent(ax);

	// range space vector
	size_t m = 1;
	CPPAD_TESTVECTOR(AD<double>) ay(m);
	ay[0] = 0.0;
	for(size_t j = 0; j < n; j++)
		ay[0] += double(j+1) * ax[0] * ax[j];

	// create f: x -> y and stop tape recording
	CppAD::ADFun<double> f(ax, ay);

	// sparsity pattern for the identity matrix
	size_t nr     = n;
	size_t nc     = n;
	size_t nnz_in = n;
	sparsity pattern_in(nr, nc, nnz_in);
	for(size_t k = 0; k < nnz_in; k++)
	{	size_t r = k;
		size_t c = k;
		pattern_in.set(k, r, c);
	}
	// compute sparsity pattern for J(x) = f'(x)
	bool transpose       = false;
	bool dependency      = false;
	bool internal_bool   = false;
	sparsity pattern_out;
	f.for_jac_sparsity(
		pattern_in, transpose, dependency, internal_bool, pattern_out
	);
	//
	// compute sparsity pattern for H(x) = f''(x)
	CPPAD_TESTVECTOR(bool) select_range(m);
	select_range[0]      = true;
	CppAD::sparse_hes_work work;
	f.rev_hes_sparsity(
		select_range, transpose, internal_bool, pattern_out
	);
	size_t nnz = pattern_out.nnz();
	ok        &= nnz == 7;
	ok        &= pattern_out.nr() == n;
	ok        &= pattern_out.nc() == n;
	{	// check results
		const SizeVector& row( pattern_out.row() );
		const SizeVector& col( pattern_out.col() );
		SizeVector row_major = pattern_out.row_major();
		//
		ok &= row[ row_major[0] ] ==  0  && col[ row_major[0] ] ==  0;
		ok &= row[ row_major[1] ] ==  0  && col[ row_major[1] ] ==  1;
		ok &= row[ row_major[2] ] ==  0  && col[ row_major[2] ] ==  2;
		ok &= row[ row_major[3] ] ==  0  && col[ row_major[3] ] ==  3;
		//
		ok &= row[ row_major[4] ] ==  1  && col[ row_major[4] ] ==  0;
		ok &= row[ row_major[5] ] ==  2  && col[ row_major[5] ] ==  0;
		ok &= row[ row_major[6] ] ==  3  && col[ row_major[6] ] ==  0;
	}
	//
	// Only interested in cross-terms. Since we are not computing rwo 0,
	// we do not need sparsity entries in row 0.
	CppAD::sparse_rc<SizeVector> subset_pattern(n, n, 3);
	for(size_t k = 0; k < 3; k++)
		subset_pattern.set(k, k+1, 0);
	CppAD::sparse_rcv<SizeVector, DoubleVector> subset( subset_pattern );
	//
	// argument and weight values for computation
	CPPAD_TESTVECTOR(double) x(n), w(m);
	for(size_t j = 0; j < n; j++)
		x[j] = double(n) / double(j+1);
	w[0] = 1.0;
	//
	std::string coloring = "cppad.general";
	size_t n_sweep = f.sparse_hes(
		x, w, subset, subset_pattern, coloring, work
	);
	ok &= n_sweep == 1;
	for(size_t k = 0; k < 3; k++)
	{	size_t i = k + 1;
		ok &= subset.val()[k] == double(i + 1);
	}
	//
	// convert subset from lower triangular to upper triangular
	for(size_t k = 0; k < 3; k++)
		subset_pattern.set(k, 0, k+1);
	subset = CppAD::sparse_rcv<SizeVector, DoubleVector>( subset_pattern );
	//
	// This will require more work because the Hessian is computed
	// column by column (not row by row).
	work.clear();
	n_sweep = f.sparse_hes(
		x, w, subset, subset_pattern, coloring, work
	);
	ok &= n_sweep == 3;
	//
	// but it will get the right answer
	for(size_t k = 0; k < 3; k++)
	{	size_t i = k + 1;
		ok &= subset.val()[k] == double(i + 1);
	}
	return ok;
}
// END C++
